Degree of Freedom in the Lorentz Transformation
Lorentz pointed out in 1899 that a relativistic space-time transformation that leaves Maxwell’s equations invariant could only be defined to within a common factor on the basis of then-existing experimental data. The present Note calls attention to the fact that Einstein’s subsequent derivation of the Lorentz transformation (LT) is based on an undeclared assumption regarding the functional dependence of this factor. Consequently, many of the unconfirmed predictions of Einstein’s special theory of relativity (SR), such as remote non-simultaneity of events and Fitzgerald-Lorentz length contraction, would lose their validity if the above assumption is shown to be incorrect. At the same time, any other choice for Lorentz’s common factor is seen to be consistent with the relativistic velocity transformation (VT). Accordingly, predictions of SR that are derived exclusively from the VT would not be affected by such a change in relativity theory. On this basis, an alternative Lorentz transformation (ALT) is defined that also satisfies Einstein’s two postulates of relativity, but incorporates the strict proportionality of the rates of moving clocks assumed in the operation of the Global Positioning System (GPS) rather than invoking the inextricable mixing of space and time coordinates predicted by the LT.